Compositionality applies to both syntax and semantics, it simply means that some property of compound expressions reduces to that of their constitutive parts. In the case of syntax the property is well-formedness, and in the case of semantics it is the "meaning". What Horst calls "stronger kind of syntax" is exactly that semantics be compositional, that is meanings of sentences, say, be reducible to meanings of subsentential units according to the syntactic structure of the sentence. In other words, this is a semantic issue, and Horst is using "syntax" here only analogically, not literally.
Semantic compositionality is the creed of the semantic representationalism common in the traditional semantics, going back to Frege and Husserl. The argument was that for language to be learnable and communicable its users must be able to generate meanings of compounds out of meanings of their atomic parts syntactically, and the meaning of atomic parts can be assigned in isolation. This argument rests however on a kind of "intelligent design fallacy": speakers do not have to master the language by learning "meanings" piece by piece, they can master it by mastering its lumps of increasing complexity (like the human eye did not evolve piece by piece, but through a sequence of wholes increasing in complexity).
Over the course of the last century representationalism came under increasing pressure from criticism by and competing pragmatist semantic theories of Wittgenstein, Quine, Davidson..., and recently Brandom. They are holistic rather than atomistic, and in them Horst's compositionality is replaced by recursivity, and his conventions by customs and practices. In Brandom's inferentialism, for example (described in Articulating Reasons):"Grasping the concept that is applied in such a making explicit is mastering its inferential use: knowing (in the practical sense of being able to distinguish, a kind of knowing how) what else one would be committing oneself to by applying the concept, what would entitle one to do so, and what would preclude such entitlement". Here is Brandom on compositionality in his response to Fodor and Lepore:
"Compositionality is a constraint on formal semantics. But, it is argued in effect, since holism is incompatible with compositionality, it serves also as a constraint on philosophical semantics... The argument that projectibility and systematicity (and hence learnability) require semantic atomism, because they require compositionality in a sense that presupposes atomism, is fallacious. It depends upon systematically overlooking the possibility of semantic theories that have the shape of the incompatibility semantics for classical and modal logical vocabulary. For although that semantics is not compositional, it is fully recursive. The semantic values of logically compound expressions are wholly determined by the semantic values of logically simpler ones. It is holistic, that is, noncompositional, in that the semantic value of a compound is not computable from the semantic values of its components. But this holism within each level of constructional complexity is entirely compatible with recursiveness between levels".